As \(\alpha _{_{1,6}}=\alpha _{_{2,6}}=0\) , the PDEs are changed into
the first type Appell PDEs. The holonomic rank of the ideal composed of the
PDEs is 3, which indicates the fundamental
solution system is constituted by three linear independent hypergeometric
functions in certain neighborhoods of regular singularities.
It is known that the fourth type Appell function cannot be imbedded into
Grassmannians [1]}. Nevertheless, including the appropriate power factor
and the corresponding transformation of the variables, the Feynman integral presented through
the fourth Appell functions [2]}, [3]} satisfies the above PDEs.
Those matrices of integer lattice permit 12 possibilities of the exponents.
Corresponding to the integer lattice \(n_{_1}E_{_3}^{(3)}+n_{_2}E_{_3}^{(2)}\) 
the choice of exponents is written as
\(&&\alpha _{_{1,3}}=1-{D\over 2}\;,\;\alpha _{_{1,6}}={D\over 2}-2\;,\;\alpha _{_{2,3}}=-1\;,\;\alpha _{_{2,6}}=0\;,\;\alpha _{_{3,3}}=2-{D\over 2},\;\alpha _{_{3,6}}=0\;,\) 
